Large-scale mean flow and inclination of isolated turbulent band in channel flow

Isolated turbulent bands observed in transitional channel flows have downstream heads and inclined bulks at a characteristic angle. In the large-scale mean flow, a $\nu$-shape vortex found at the head elongates into the bulk part, forming a pair of counter-rotating vortex tube structures. It is revealed numerically and theoretically that the head and the bulk convection velocities reflect the obliquely forward and the backward self-induced velocities of the $\nu$-shape vortex and the vortex tube pair, respectively, and the difference between these convection velocities provides a restoring angular momentum to retain the characteristic inclination angle through a self-adjustment process.